CUET · MATHS · PYQ PAPER 2023
Derivative of \(\cos \left(\sin \left(x^2\right)\right)\) with respect to x is:
- A \(2 x \sin \left(x^2\right) \cos \left(\cos \left(x^2\right)\right)\)
- B \(-2 x \sin \left(x^2\right) \cos \left(\cos \left(x^2\right)\right)\)
- C \(-2 x \cos \left(x^2\right) \sin \left(\sin \left(x^2\right)\right)\)
- D \(2 x \cos \left(x^2\right) \sin \left(\cos \left(x^2\right)\right)\)
Answer & Solution
Correct Answer
(C) \(-2 x \cos \left(x^2\right) \sin \left(\sin \left(x^2\right)\right)\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{dx} \left(\cos \left(\sin \left(x^2\right)\right)\right) = -\sin \left(\sin \left(x^2\right)\right) \cdot \cos \left(x^2\right) \cdot 2x\) \(= -2x \cos \left(x^2\right) \sin \left(\sin \left(x^2\right)\right)\)
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